On the invertibility of mappings arising in 2D grid generation problems

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Clement, Ph. and Hagmeijer, R. and Sweers, G. (1996) On the invertibility of mappings arising in 2D grid generation problems. Numerische Mathematik, 73 (1). pp. 37-52. ISSN 0029-599X

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Abstract:In adapting a grid for a Computational Fluid Dynamics problem one uses a mapping from the unit square onto itself that is the solution of an elliptic partial differential equation with rapidly varying coefficients. For a regular discretization this mapping has to be invertible. We will show that such result holds for general elliptic operators (in two dimensions). The Carleman-Hartman-Wintner Theorem will be fundamental in our proof. We will also explain why such a general result cannot be expected to hold for the (three-dimensional) cube.
Item Type:Article
Copyright:© 1996 Springer
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Engineering Technology (CTW)
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Link to this item:http://purl.utwente.nl/publications/58056
Official URL:http://dx.doi.org/10.1007/s002110050182
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